Boston Red Sox
New York Mets
New York Yankees
Toronto Blue Jays
No one in their right mind could argue that the Red Sox/Yankees rivalry hasn't been the best in all of baseball. Keeping the pair together is clearly a no-brainer. Another great rivalry is the Subway Series, the games between the Yankees and the Mets. The Yankees often get the better of Mets(see 2000 World Series), and have by far had more success, but each teams fans hate the other team very much. A rivalry that could grow from this alignment would be that of the Orioles vs. the Nationals. The two ballparks are about an hours drive away from each other, and each team looks to be on the rise, which should mean some competitive baseball. I had to throw in the Blue Jays here because they are closest to the New York and don't really have any rivalries as they have been going through a mediocre couple of years.
Chicago White Sox
Kansas City Royals
St. Louis Cardinals
This division becomes the smallest division. The Cubs are the stars as far as rivalries in this division are concerned, with fans hating both the Cardinals and the White Sox. The White Sox are familiar foes for the Royals. Those Royals have been getting whooped around by Cardinals(and every other team in the MLB) but the closeness of the two teams has produced a good rivalry between the two teams.
Los Angeles Angles of Anaheim
Los Angeles Dodgers
San Diego Padres
San Francisco Giants
This division features the all five California state teams and the Mariners, who most people mistake as being from the nation's capitol. The existing rivalries between the Angels, Athletics, and Mariners carry over from the original AL West, as does the rivalries between the Dodgers, Giants, and Padres. This division would promote the rivalries between the two Bay Area teams and the two Los Angeles teams(even though the Angels aren't really in LA.) San Diego isn't to far from Los Angeles but is quite a ride to and from the Bay area. Any team traveling to Seattle will not enjoy it, no matter what division they're in. The same could be said for the Mariners traveling.
Tampa Bay Rays
This was by far the toughest division to make. The only three southeast teams were not enough to grant their own division, so I was forced into including the two Pennsylvania teams. The two intra-state rivalries between the Marlins/Rays and the Phillies/Pirates would be good though it still remains unknown when the Pirates will finally be a formidable foe. Also the already existing rivalries between the Phillies/Marlins/Braves from the original NL East would easily carry over.
The carryover of rivalries between the Indians/Tigers/Twins will be familiar along with that of the Brewers/Reds. The intra-state rivalry will take place in Ohio, between the Reds and Indians. Also, the rivalry that brewing between the Brewers and the Twins will have a fire lit under it and the Milwaukee could also look forward to a rivalry with the Tigers.
The Rangers are the team least familiar with the others as the others are all from the NL West, but they do have a strong pre-existing rivalry with same state Astros. The Rockies/Diamondbacks/Astros will all carryover hatred fro the other team and the Ranger fans will have to grow a hatred for the Diamondbacks and Rockies.
Of course, inter-league play would remain, allowing for old division rivalries to be revisited. This alignment is heavy on teams that are in the same state being in the same division. If not most teams will have a relatively small amount of time for games played within their divisions, excluding some teams that will have to travel to and from Atlanta, Seattle, and Florida. The competitive balance isn't really there, which is most evident in AL West and NL East. Those division hold four teams that are currently tough competitors. Despite that, the promotion of geographical realignment could lead to teams saving more money on trips and could increase revenue as fans would be more likely to make an hour or so drive to see a road game.